Data-driven extraction and phenomenology of eccentric harmonics in eccentric spinning binary black hole mergers

Abstract

Newtonian and post-Newtonian (PN) calculations indicate that the phenomenology of eccentric binary black hole (BBH) merger waveforms is significantly more complex than that of their quasi-circular counterparts. Each spherical harmonic mode of the radiation can be further decomposed into several eccentricity-induced components, referred to as eccentric harmonics. Unlike the (cumulative) spherical harmonic modes, these constituent eccentric harmonics exhibit monotonically time-varying amplitudes and frequencies. However, these eccentric harmonics are not directly accessible in numerical relativity (NR) simulations or current eccentric waveform models. Using the recently developed data-driven framework gwMiner, which combines singular value decomposition, input from post-Newtonian theory, and signal processing techniques, we extract eccentric harmonics from eccentric, aligned-spin waveforms for six different spherical harmonic modes: (2,1), (2,2), (3,2), (3,3), (4,3), (4,4). We demonstrate that the phase (frequency) of each eccentric harmonic takes the form $j\ddot{I}{•}_{\ell ,m,\hat{I}»}+\ddot{I}{•}_{\ell ,m,\mathrm{ecc}}$ ($j{f}_{\ell ,m,\hat{I}»}+f_{\ell ,m,\mathrm{ecc}}$), where $\ddot{I}{•}_{\ell ,m,\hat{I}»}$ ($f_{\ell ,m,\hat{I}»}$) corresponds to the secular orbital phase (frequency), and $\ddot{I}{•}_{\ell ,m,\mathrm{ecc}}$ ($f_{\ell ,m,\mathrm{ecc}}$) is an additional contribution that depends solely on the eccentricity. We further find that $\ddot{I}{•}_{\ell ,m,\hat{I}»}$ is the same across different spherical harmonic modes $(\ell ,m)$, whereas the eccentric correction term $\ddot{I}{•}_{\ell ,m,\mathrm{ecc}}$ scales with $\ell$. Using effective-one-body dynamics, we further show that $\ddot{I}{•}_{\ell ,m,\hat{I}»}$ is nothing but the relativistic anomaly and $\ddot{I}{•}_{\ell ,m,\mathrm{ecc}}$ is related to the precession advances.